# How much light is too much?

A mage has created an amulet of light. It shines light from one side, and the user is capable of controlling the color and intensity of that light.

In an effort to avoid abuse, the mage has limited the amulet to only produce wavelengths in the visible range.

Perhaps less cleverly, they did not think to put a limit on the amount of light that can be produced at once.

A foolish thief has gotten their hands on the amulet and started cranking up the intensity. At what point will their actions start to cause noticeable physical effects, and what will those effects be?

My guess is that, at some point, objects will become hot enough to catch fire, radiation pressure will start pushing objects (and the amulet) around, and light will shine through normally opaque objects. Are these guesses correct, and are there any other dangers my thief should be wary of?

Bonus: Are some wavelengths of visible light safer than others? Which are they?

• Might want to add the magic tag or some pedant'll come along and ask where the energy's coming from and start quoting limits of matter energy conversion of a amulet's mass. Alternativley, say it comes from subspace or the next universe over. Maybe the question is valid as-is, what do people think? – Don Qualm Feb 24 at 19:31
• No, I don't think that the magic tag is a good fit for this one. Yes, I used 'a wizard did it' to create the scenario, but there shouldn't be any magic in the answers. "How the light is generated" is not within the scope of the question. – Arcanist Lupus Feb 24 at 19:39
• I'll go with that argument, sounds convincing to me. - Sorry to get all meta on you, I'm happy now though. – Don Qualm Feb 24 at 19:41
• Please don't make edits that invalidate existing answers. – Renan Feb 24 at 21:08
• The title made me thing that this should be a what-if question. Actually, it already is: what-if.xkcd.com/13 – Baldrickk Feb 25 at 10:33

If the light coming out of the amulet is well collimated (i.e. it can form a narrow beam that does not disperse - like a laser) and the light is emitted continuously rather than in pulses, then what it does will depending on the aperture (i.e. the cross sectional area) of the amulet.

Assuming a diameter of 2-3 cm (wristwatch or locket sized), an intensity of tens to hundreds of watts could cause temporary/permanent blindness if pointed at someone's eyes, and kilowatts would be enough to set light to a flammable target. 104 of W would cut through stuff. If the emission moves up to megawatts then the surface of the target will heat up and ablate so rapidly that it will effectively act like an explosion - the target might be thrown backwards but this is due to evaporation at the super-heated surface, not radiation pressure. Somewhere around 1012-1014W, the air in the path of the beam would almost instantaneously ionize and absorb a significant fraction of the beam energy. This would be bad for the holder of the amulet as it means that the air directly in front of them would glow more brightly than the surface of the sun - the amulet holder would get very bad sun-burn.

At vastly higher energy the beam could convert materials to plasma, break up atomic nuclei and eventually convert all matter to a quark-soup like that found in the first few nanoseconds of the big-bang. Radiation pressure would now be evident - but only if you used the amulet in a vacuum as the reaction with any nearby matter would overwhelm the effect otherwise. At stupidly higher energy, you might reach the Plank limit beyond which physicists can only guess - but more likely the energy density would be so great that local space along the beam would instantly collapse into a black hole.

If the amulet fires out a narrow beam - 0.1 mm diameter perhaps, then all the power requirements drop by around 4 orders of magnitude. Probably harder to blind an enemy then but it would still be effective for cutting/drilling through things at a distance. If it was pulsed, then the relative danger to the user may be reduced.

If the amulet fired out a dispersed wide angle multi-frequency beam like a hand-held torch, then bad things would happen to the wielder (the sun-burn and explosions resulting from heating of the air immediately in front of the amulet) before it would do much harm to any target more than a few tens of metres away.

If the light is not coherent, all the things described for the coherent beam would still happen, but at higher energy required for an effect on a target, and a lower energy required for the 'effects' on the wielder.

• @Penguino Nice progression and details. +1. Formatting of first paragraph - meh, but that doesn't matter. – Don Qualm Feb 24 at 21:14
• "What if we tried more power?" – ununseti Feb 25 at 3:13
• @aquirdturtle Coherent = laser. Not coherent = lightbulb. – immibis Feb 25 at 4:36
• @aquirdturtle I can't find anything about incoherent lasers, and lots of stuff suggesting that they do emit coherent light. Also, obviously he's not listing all sufficient conditions, since lightbulbs require more than just incoherence too. – JMac Feb 25 at 16:04
• It's very easy to make an incoherent laser, you take a gain medium and illuminate it with incoherent light. You have lasing, i.e. light amplification by stimulated emission of radiation, but the output is incoherent because the input was incoherent. It's also very easy to take an incoherent source and make it both spatially and temporally coherent by appropriate spatial and frequency filtering. Most lasers are coherent, as many applications make use of the coherence, but it's definitely not necessary. – aquirdturtle Feb 25 at 20:13

### Black Holes?

You amulet can generate black holes. Given the radius of your amulet $$R_s$$ we can calculate the amount of mass necessary to collapse it into a black hole.

$$M = \frac{c^2}{2G}R_s$$

But your amulet produces light not mass. Lucky, Einstein can help us with its mass energy equivalence:

$$E = mc^2$$

So, we need:

$$E = c^2\frac{c^2}{2G}R_s$$

That is the amount of energy you need to make a black hole. If your intensity were that amount of watts (and the light didn't move), in a single second you would be able to produce a black hole.

If you want the radiant intensity, knowing that $$4\pi$$ Steradian is a sphere:

$$W/sr = \frac{c^2\frac{c^2}{2G}R_s}{4\pi}$$

You need that amount of W/sr (also know as watts per steradian).

Or, given a candela is $$\frac{1}{683}$$ W/sr:

$$\text{Cd} = 683*\frac{c^2\frac{c^2}{2G}R_s}{4\pi}$$

That is the amount of light need to perform a black hole. But, taking into account that light moves very fast, you should rather produce that output in a single burst of light instead of over a single second. Otherwise, you will need better maths.

• +1. The bit about no limit kinda asks for this. – Renan Feb 24 at 22:43
• "Your amulet makes so much light it has started absorbing it" – Asoub Feb 25 at 9:52
• Quick calculation shows that energy output need to be about 1×10E42 watts. For comparison, Sun's energy output is 3.828×10E26, and the entire Milky Way's 8×10E36, and the brightest known quasar is 2×10E41. – Alexander Feb 25 at 20:22
• @Alexander, impressive! That is a powerful amulet of light! Can I ask which size of amulet did you used for the calculations? – Ender Look Feb 25 at 20:25
• That would be about 6-7 cm big. My calculation is not precise, I wanted to see just the order of magnitude. – Alexander Feb 25 at 20:54

Somewhere in the kilowatt range nearby objects will start heating appreciably and possibly even catching fire (see for example Wicked Laser's FlashTorch). It will depend on their reflectivity, the material they're made of, beam dwell time, and so on.

Much sooner than that, you'll get temporary flash blindness from reflected light. I haven't been able to find a reliable source on the intensity required, but I came up with an approximate ballpark figure of 14000 lumen (that's around 150 W with high-efficiency LEDs, which the magic device appear to resemble) from data on nuclear explosions.

Radiation pressure doesn't come into play until much, much later.

A big "if" hangs on the quality of light. It might be in the visible octave, and still be almost-monochromatic coherent laser light.

• You might also address the issue of coherence. If the light is coherent, both direct and reflected light will run a serious risk of inducing blindness at much lower (sub-watt) levels. – WhatRoughBeast Feb 24 at 20:08
• @ArcanistLupus I rolled the edit back since it invalidated the answers already given. – Renan Feb 24 at 21:10

At what point will their actions start to cause noticeable physical affects, and what will those effects be?

Projecting light is itself a physical effect. Starting at a flux of 0.0001 flux in an dark place, the light will be enough for the naked eye to see, which is equivalent to starlight on a moonless night.

But of course you didn't mean that.

The effects visible light has on things, besides making them visible to us, depend on the target. In general visible light can slow down or more usually speed up chemical reactions (think of polaroids) and warm stuff up.

Regular laser pointers are usually within the 3 to 5 miliwatt range. It can blind people. There is a chronic mental disease that causes people to point such lasers at aircraft for kicks, which is how you can use a very little amount of light to take hundreds of lives in a very grim way.

A 100 miliwatt laser pointer with a tight beam width at close range can set fire to matches and gasoline, so you may emulate that. More power makes it easier and faster to set stuff on fire.

• A really good point. The effect of visible light on plants (for example) is pretty pronounced!! – Joe Bloggs Feb 24 at 20:24
• Plus one for the chronic mental disease, although I think that it may be a manifestation of innate evilness. – AlexP Feb 24 at 21:18
• "There is a chronic mental disease that causes people to point such lasers at aircraft for kicks" - I think it's called, "being male and a jerk." – WhatRoughBeast Feb 24 at 21:23
• 3 and 5mW lasers are not going to blind people. The only reason some cheap Chinese-made 5mW lasers have caused eye damage is because the output was actually far higher. But a single 3 or 5mW red laser, if it's really only that strong, would be harmless to anyone whose eyes are functioning normally. – forest Feb 25 at 2:12
• @Renan If you paid me for my time and gave me a pointer certified to be no more than 5 mW, then sure. – forest Feb 25 at 10:33

In an effort to avoid abuse, the mage has limited the amulet to only produce wavelengths in the visible range.

Some other limitations to consider:

The amulet would have to be tied to a power source in some way.
Either that power source is unlimited or limited. Limited would give a fixed number of charges/uses. Unlimited could still be constrained to a recharging period.

You also could choose to limit the output to the amount of energy that can flow through from that power source to the amulet (which keeps black holes and mega-watt pulse lasers from being a possibility).

I expect you're looking for the more entertaining answers already given, but this may help if you're looking for balance.

• I'm not looking for balance. I'm trying to understand the ramifications of the specifically unbalanced situation I created. – Arcanist Lupus Feb 25 at 20:14